A class of pseudoinverse-free greedy block nonlinear Kaczmarz methods for nonlinear systems of equations

Abstract

<abstract><p>In this research, we constructed a class of nonlinear greedy average block Kaczmarz methods to solve nonlinear problems without computing the Moore-Penrose pseudoinverse of the Jacobian matrix. These kinds of methods adopt the average technique of the Gaussian Kaczmarz method and combine the greedy strategy, which greatly reduces the amount of computation. The local convergence analysis and numerical experiments of the proposed methods are given. The numerical results show the effectiveness of the proposed methods.</p></abstract>